## PDE and Differential Geometry Seminar

# Measures of maximal entropy for suspension flows over the full shift

## Tamara Kucherenko (City College of New York)

### Monday, December 3, 2018
2:30 pm

MONT 214 (Storrs)

We consider suspension flows with continuous roof function over the full shift on a finite alphabet. For any positive entropy subshift of finite type, we show there exists a roof function such that the measures of maximal entropy for the suspension flow over the full shift are exactly the lifts of the measures of maximal entropy for the subshift. In the case when the subshift is transitive, this gives a unique measure of maximal entropy for the flow which is not fully supported. If the subshift has more than one transitive component, all with the same entropy, this gives explicit examples of suspension flows over the full shift with multiple measures of maximal entropy. This contrasts with the case of a Holder continuous roof function where it is well known the measure of maximal entropy is unique and fully supported. This is a joint work with Dan Thompson.